The present invention is generally related to signal processing for a radar system for motion compensation and target focusing.
The fast and accurate estimation of target range, range rate (i.e., radial velocity), and acceleration from sampled radar return signals is necessary for some radar applications. Joint estimation of these target motion parameters is an important precursor to motion compensation for high resolution spectral analysis of targets and synthetic aperture radar (SAR) or inverse synthetic aperture radar (ISAR) processing. The joint estimation of target motion parameters is also applicable in orbit determination of high altitude satellites, which typically require integration over long pulse trains for reliable detection and position measurement.
Many conventional radar systems attempt to accurately and expeditiously estimate target motion parameters. Some techniques used by conventional systems include the maximum entropy technique, the phase-gradient autofocus technique, and the phase difference autofocus technique, among others.
Maximum likelihood estimation (MLE) is a popular statistical method used to calculate the best way of fitting a mathematical model to some data. Modeling real data by estimating a maximum likelihood offers a way of tuning the free parameters of a model to provide an optimum fit.
Thus, some conventional systems have utilized the MLE technique for the determination of target motion parameters. The MLE in this case reduces to finding the maximum of a nonlinear 3-dimensional (3D) likelihood function. The range-velocity projection of the likelihood function behaves like an ambiguity function with a mainlobe accompanied by surrounding sidelobes that introduce many local maxima. The extent of the mainlobe is given by the radar range and velocity resolution formulas, known to those skilled in the art.
The conventional range and velocity resolution formulas, assuming no coupling between range and velocity estimation, are respectively given by c/(2BW) and (λ/2)/TDWELL, where c is the speed of light, BW is the bandwidth of the radar, λ is the wavelength at RF, and TDWELL is the dwell duration. Because of the small area c/(2BW) by (λ/2)/TDWELL of the mainlobe and the abundance of local optima, searching for the global maximum of the 3D function typically requires an exceedingly large number of computations.
Previous efforts to reduce the number of required computations for the MLE technique generally include the calculation of a priori bounds on the mean square error for the MLE of motion parameters or by non-coherent methods that initialize the MLE. However, these efforts have resulted in limited success. As such, prior attempts to improve the estimation of target motion parameters suffer from one or more of the following: prohibitively large numbers of computations, limited robustness, and limited accuracy.
For further background material, see Theagenis J. Abatzoglou and Gregory O. Gheen, Range, Radial Velocity, and Acceleration MLE using Radar LFM Pulse Train, IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS, Vol. 34, No. 4, October 1998, incorporated herein by reference in its entirety.